This paper reports a measurement of the cross section for the pair production of top quarks in p (p) over bar collisions at root s = 1.96 TeV at the Fermilab Tevatron. The data were collected from the CDF run II detector in a set of runs with a total integrated luminosity of 1.1 fb(-1). The cross section is measured in the dilepton channel, the subset of t (t) over bar events in which both top quarks decay through t -> Wb -> l nu b, where l = e, mu, or tau. The lepton pair is reconstructed as one identified electron or muon and one isolated track. The use of an isolated track to identify the second lepton increases the t (t) over bar acceptance, particularly for the case in which one W decays as W -> tau nu. The purity of the sample may be further improved at the cost of a reduction in the number of signal events, by requiring an identified b jet. We present the results of measurements performed with and without the request of an identified b jet. The former is the first published CDF result for which a b-jet requirement is added to the dilepton selection. In the CDF data there are 129 pretag lepton + track candidate events, of which 69 are tagged. With the tagging information, the sample is divided into tagged and untagged subsamples, and a combined cross section is calculated by maximizing a likelihood. The result is sigma(t (t) over bar) = 9.6 +/- 1.2(stat)(-0.5)(+0.6)(sys) +/- 0.6(lum) pb, assuming a branching ratio of BR(W -> l nu) = 10.8% and a top mass of m(t) = 175 GeV/c(2). RI Ruiz, Alberto/E-4473-2011; Robson, Aidan/G-1087-2011; De Cecco, Sandro/B-1016-2012; St.Denis, Richard/C-8997-2012; Prokoshin, Fedor/E-2795-2012